The volume of a growing tropical fruit, V(x)V(x)V(x) in cm3\text{cm}^3cm3, after x x\,x weeks is modeled by the function
V(x)=(2+kx4)7 V(x) = \left(2 + \frac{kx}{4}\right)^7 V(x)=(2+4kx)7where k k\,k is a non-zero constant.
Find the first 4 terms, in ascending powers of xxx, of the binomial expansion of V(x)V(x)V(x). Give each term in simplest form.
Given that the coefficients of xxx, x2x^2x2, and x3 x^3\,x3 in this expansion form the first three terms of an arithmetic progression,
find, using algebra, the possible values of kkk.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
